1. Field of the Invention
The present invention relates generally to a decoding method and apparatus for a receiver in a mobile communication system. More particularly, the present invention relates to a log-likelihood ratio (LLR) calculation method and apparatus for decoding in a receiver for a mobile communication system using Quadrature Phase Shift Keying (QPSK) or Quadrature Amplitude Modulation (QAM).
2. Description of the Related Art
In general, modulation refers to a process of converting a signal into a format suitable for a transmission channel using a carrier in order to transmit the signal to a desired destination without error. Among modulation schemes, a modulation scheme of shifting a phase of the carrier according to a digital transmission signal is called “Phase Shift Keying (PSK)”. Many communication systems use QPSK having an extended concept of PSK, or Binary PSK (BPSK) in which there is provided a 180°-phase difference between carriers.
While BPSK distinguishes only two kinds of signals, that is ‘1’ and ‘0’, QPSK distinguishes four kinds of signals, including ‘00’, ‘01’, ‘10’ and ‘11’. Theoretically, QPSK doubles BSPK in terms of the amount of data that can be transmitted for a specific time because QPSK can transmit four kinds of 2-bit digital signals. In other words, while BPSK shifts a phase of the carrier by 180° during transmission, QPSK shifts a phase of the carrier by 90° and transmits 4 signals, thereby increasing the amount of transmission data.
Another typical modulation scheme for transmitting a large volume of data is QAM, which modulates a digital signal by changing an amplitude and phase of the signal. Because QAM, unlike PSK, BPSK and QPSK, uses not only the phase of the signal but also the amplitude of the signal as parameters, it can simultaneously transmit a large amount of digital data and uses as many signal coordinates as a multiplier of 2. The QAM scheme is classified into 16QAM, 64QAM and 256QAM according to the number of signal coordinates.
For example, in the case of 16QAM, digital signals quantized in 16 levels are scattered over 16 signal coordinates in an I/Q plot. That is, 16QAM can transmit 4-bit binary digital signals per coordinate though 16 signal domains which are different in phase and amplitude. A receiver for a communication system using QAM demodulates a received signal into its original signal by observing on which domain the received signal is located on the basis of a boundary distinguishing the signal coordinates.
Due to the increase in the amount of communication data, research into communication systems is being conducted to transmit the increasing amount of data by systems having limited bandwidth. As a result, although the conventional communication system transmits 2 bits per symbol using QPSK, the more recent communication systems can transmit 4 bits per symbol using 16QAM and 6 bits per symbol using 64QAM. That is, the increase in modulation order of QAM increases the number of bits per transmission symbol.
However, the signals transmitted using QPSK or QAM have a high reception error rate, as they are distorted through radio channels. In order to decrease the error rate, a transmitter commonly uses turbo coding. A receiver for a communication system using turbo coding calculates a log-likelihood ratio (LLR) from the received signal modulated with QPSK or QAM, in a decoding process, and performs iterative decoding depending on the calculated LLR, thereby improving decoding reliability.
The LLR, which is a probability value provided as priori information for the next decoding in the iterative decoding process, increases its calculation load as a modulation order of transmission symbols increases, causing an increase in the load on the receiver.
A description will now be made of a conventional LLR calculation method for a QAM decoder by way of example.
An LLR used in the QAM decoder is calculated using Equation (1) below.
                                                        LLR              =                              Log                (                                                                            ∑                      i                                        ⁢                                          p                      ⁡                                              (                                                                              s                            i                            0                                                    |                          r                                                )                                                                                                                        ∑                      i                                        ⁢                                          p                      ⁡                                              (                                                                              s                            i                            1                                                    |                          r                                                )                                                                                            )                                                                                        =                              Log                (                                                                            ∑                      i                                        ⁢                                                                                            p                          ⁡                                                      (                                                          r                              |                                                              s                                i                                0                                                                                      )                                                                          ⁢                                                                                                  ⁢                                                  p                          ⁡                                                      (                                                          s                              i                              0                                                        )                                                                                                                      p                        ⁡                                                  (                          r                          )                                                                                                                                                ∑                      i                                        ⁢                                                                                            p                          ⁡                                                      (                                                          r                              |                                                              s                                i                                1                                                                                      )                                                                          ⁢                                                                                                  ⁢                                                  p                          ⁡                                                      (                                                          s                              i                              1                                                        )                                                                                                                      p                        ⁡                                                  (                          r                          )                                                                                                                    )                                                                                        =                              Log                (                                                                            ∑                      i                                        ⁢                                          p                      ⁡                                              (                                                  r                          |                                                      s                            i                            0                                                                          )                                                                                                                        ∑                      i                                        ⁢                                          p                      ⁡                                              (                                                  r                          |                                                      s                            i                            1                                                                          )                                                                                            )                                                                        Equation        ⁢                                  ⁢                  (          1          )                    
In Equation (1), p(si0|r) and p(si1|r) denote aposteriory probabilities when signal points si corresponding to a bit ‘0’ and a bit ‘1’ in signal coordinates of a constellation are transmitted in response to a received signal r. Further, p(si0) and p(si1) denote probabilities that signal points si corresponding to a bit ‘0’ and a bit ‘1’ will occur, respectively. Herein, it is assumed that the probabilities are equal to each other.
In the case of a simple QPSK scheme, a transmitter transmits one of 4 signal points on a constellation per every 2 bits, and a receiver calculates LLRs using the aposteriory probabilities on the assumption that the reception signal and the signal point on the constellation have been transmitted. In this case, one of the two bits defines one of two signal points on a real axis in the constellation, and the other one bit defines the other one of the two signal points on an imaginary axis in the constellation. Therefore, the receiver is allowed to calculate an LLR using only one signal point associated with the corresponding bit in the process of calculating the aposteriory probability for each bit.
FIG. 1 is a diagram illustrating a gray-decoded QPSK constellation in a general mobile communication system. When the QPSK constellation of FIG. 1 is used, LLRs for 2 bits of b0 and b1 are expressed as Equation (2) below, in which it is assumed that channel noise is additive white Gaussian noise (AWGN).
                                                                        LLR                b0                            =                              log                ⁢                                                                  ⁢                                                      exp                    (                                          -                                                                                                    (                                                                                          RE                                ⁡                                                                  [                                  r                                  ]                                                                                            -                                                              s                                0                                                                                      )                                                    2                                                                          2                          ⁢                                                                                                          ⁢                                                      σ                            2                                                                                                                )                                                        exp                    (                                          -                                                                                                    (                                                                                          RE                                ⁡                                                                  [                                  r                                  ]                                                                                            -                                                              s                                1                                                                                      )                                                    2                                                                          2                          ⁢                                                                                                          ⁢                                                      σ                            2                                                                                                                )                                                                                                                                                                      ⁢                              =                                                                            RE                      ⁡                                              [                        r                        ]                                                              ·                                          (                                                                        s                          0                                                -                                                  s                          1                                                                    )                                                                            σ                    2                                                                                                                                                                      ⁢                              =                                                                            RE                      ⁡                                              [                        r                        ]                                                              ·                                          (                                              -                        2                                            )                                                                            σ                    2                                                                                                                          if              ⁢                                                          ⁢                              (                                                                            s                      0                                        =                                          -                      1                                                        ,                                                            s                      1                                        =                    1                                                  )                                                                                                        LLR                b1                            =                              log                ⁢                                                                  ⁢                                                      exp                    (                                          -                                                                                                    (                                                                                          IM                                ⁡                                                                  [                                  r                                  ]                                                                                            -                                                              s                                0                                                                                      )                                                    2                                                                          2                          ⁢                                                                                                          ⁢                                                      σ                            2                                                                                                                )                                                        exp                    (                                          -                                                                                                    (                                                                                          IM                                ⁡                                                                  [                                  r                                  ]                                                                                            -                                                              s                                1                                                                                      )                                                    2                                                                          2                          ⁢                                                                                                          ⁢                                                      σ                            2                                                                                                                )                                                                                                                                                                      ⁢                              =                                                                            IM                      ⁡                                              [                        r                        ]                                                              ·                                          (                                                                        s                          0                                                -                                                  s                          1                                                                    )                                                                            σ                    2                                                                                                                                                                      ⁢                              =                                                                            IM                      ⁡                                              [                        r                        ]                                                              ·                                          (                                              -                        2                                            )                                                                            σ                    2                                                                                                                          if              ⁢                                                          ⁢                              (                                                                            s                      0                                        =                                          -                      1                                                        ,                                                            s                      1                                        =                    1                                                  )                                                                        Equation        ⁢                                  ⁢                  (          2          )                    
However, in the case of 16QAM, a transmitter selects 16 4-bit signal points in a constellation, and a receiver calculates LLRs using both of the 2 signal points in the process of calculating aposteriory probabilities, as there are 2 signal points associated with each bit, thereby increasing its calculation load.
FIG. 2 is a diagram illustrating a gray-decoded 16QAM constellation in a general mobile communication system. When the conventional 16QAM constellation of FIG. 2 is used, LLRs for b0, b1, b2 and b3 representing signal points in the constellation are calculated using Equation (3) below.
                                                                        LLR                b0                            =                              log                ⁢                                                                  ⁢                                                                            ∑                      i                                        ⁢                                          p                      ⁡                                              (                                                                              real                            ⁡                                                          (                              r                              )                                                                                |                                                      s                            i                            0                                                                          )                                                                                                                        ∑                      i                                        ⁢                                          p                      ⁡                                              (                                                                              real                            ⁡                                                          (                              r                              )                                                                                |                                                      s                            i                            1                                                                          )                                                                                                                                                                                                                ⁢                              =                                  log                  ⁢                                                                          ⁢                                                                                    exp                        (                                                  -                                                                                                                    (                                                                                                      real                                    ⁡                                                                          (                                      r                                      )                                                                                                        -                                                                      s                                    0                                    0                                                                                                  )                                                            2                                                                                      2                              ⁢                                                                                                                          ⁢                                                              σ                                2                                                                                                                                    )                                            +                                              exp                        (                                                  -                                                                                                                    (                                                                                                      real                                    ⁡                                                                          (                                      r                                      )                                                                                                        -                                                                      s                                    1                                    0                                                                                                  )                                                            2                                                                                      2                              ⁢                                                                                                                          ⁢                                                              σ                                2                                                                                                                                    )                                                                                                            exp                        (                                                  -                                                                                                                    (                                                                                                      real                                    ⁡                                                                          (                                      r                                      )                                                                                                        -                                                                      s                                    0                                    1                                                                                                  )                                                            2                                                                                      2                              ⁢                                                                                                                          ⁢                                                              σ                                2                                                                                                                                    )                                            +                                              exp                        (                                                  -                                                                                                                    (                                                                                                      real                                    ⁡                                                                          (                                      r                                      )                                                                                                        -                                                                      s                                    1                                    1                                                                                                  )                                                            2                                                                                      2                              ⁢                                                                                                                          ⁢                                                              σ                                2                                                                                                                                    )                                                                                                                                                                                                                ⁢                              =                                  log                  ⁢                                                                          ⁢                                                                                    exp                        (                                                  -                                                                                                                    (                                                                                                      real                                    ⁡                                                                          (                                      r                                      )                                                                                                        -                                                                      (                                                                          -                                      3                                                                        )                                                                                                  )                                                            2                                                                                      2                              ⁢                                                                                                                          ⁢                                                              σ                                2                                                                                                                                    )                                            +                                              exp                        (                                                  -                                                                                                                    (                                                                                                      real                                    ⁡                                                                          (                                      r                                      )                                                                                                        -                                                                      (                                                                          -                                      1                                                                        )                                                                                                  )                                                            2                                                                                      2                              ⁢                                                                                                                          ⁢                                                              σ                                2                                                                                                                                    )                                                                                                            exp                        (                                                  -                                                                                                                    (                                                                                                      real                                    ⁡                                                                          (                                      r                                      )                                                                                                        -                                                                      (                                                                          +                                      1                                                                        )                                                                                                  )                                                            2                                                                                      2                              ⁢                                                                                                                          ⁢                                                              σ                                2                                                                                                                                    )                                            +                                              exp                        (                                                  -                                                                                                                    (                                                                                                      real                                    ⁡                                                                          (                                      r                                      )                                                                                                        -                                                                      (                                                                          +                                      3                                                                        )                                                                                                  )                                                            2                                                                                      2                              ⁢                                                                                                                          ⁢                                                              σ                                2                                                                                                                                    )                                                                                                                                                                                    LLR                b1                            =                              log                ⁢                                                                  ⁢                                                                            exp                      (                                              -                                                                                                            (                                                                                                real                                  ⁡                                                                      (                                    r                                    )                                                                                                  -                                                                  (                                                                      -                                    3                                                                    )                                                                                            )                                                        2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                        +                                          exp                      (                                              -                                                                                                            (                                                                                                real                                  ⁡                                                                      (                                    r                                    )                                                                                                  -                                                                  (                                                                      +                                    3                                                                    )                                                                                            )                                                        2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                                                                                  exp                      (                                              -                                                                                                            (                                                                                                real                                  ⁡                                                                      (                                    r                                    )                                                                                                  -                                                                  (                                                                      -                                    1                                                                    )                                                                                            )                                                        2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                        +                                          exp                      (                                              -                                                                                                            (                                                                                                real                                  ⁡                                                                      (                                    r                                    )                                                                                                  -                                                                  (                                                                      +                                    1                                                                    )                                                                                            )                                                        2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                                                                                                                                              LLR                b2                            =                              log                ⁢                                                                  ⁢                                                                            exp                      (                                              -                                                                                                            (                                                                                                imag                                  ⁡                                                                      (                                    r                                    )                                                                                                  -                                                                  (                                                                      -                                    3                                                                    )                                                                                            )                                                        2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                        +                                          exp                      (                                              -                                                                                                            (                                                                                                imag                                  ⁡                                                                      (                                    r                                    )                                                                                                  -                                                                  (                                                                      -                                    1                                                                    )                                                                                            )                                                        2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                                                                                  exp                      (                                              -                                                                                                            (                                                                                                imag                                  ⁡                                                                      (                                    r                                    )                                                                                                  -                                                                  (                                                                      +                                    1                                                                    )                                                                                            )                                                        2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                        +                                          exp                      (                                              -                                                                                                            (                                                                                                imag                                  ⁡                                                                      (                                    r                                    )                                                                                                  -                                                                  (                                                                      +                                    3                                                                    )                                                                                            )                                                        2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                                                                                                                                              LLR                b3                            =                              log                ⁢                                                                  ⁢                                                                            exp                      (                                              -                                                                                                            (                                                                                                imag                                  ⁡                                                                      (                                    r                                    )                                                                                                  -                                                                  (                                                                      -                                    3                                                                    )                                                                                            )                                                        2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                        +                                          exp                      (                                              -                                                                                                            (                                                                                                imag                                  ⁡                                                                      (                                    r                                    )                                                                                                  -                                                                  (                                                                      +                                    3                                                                    )                                                                                            )                                                        2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                                                                                  exp                      (                                              -                                                                                                            (                                                                                                imag                                  ⁡                                                                      (                                    r                                    )                                                                                                  -                                                                  (                                                                      -                                    1                                                                    )                                                                                            )                                                        2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                        +                                          exp                      (                                              -                                                                                                            (                                                                                                imag                                  ⁡                                                                      (                                    r                                    )                                                                                                  -                                                                  (                                                                      +                                    1                                                                    )                                                                                            )                                                        2                                                                                2                            ⁢                                                                                                                  ⁢                                                          σ                              2                                                                                                                          )                                                                                                                              Equation        ⁢                                  ⁢                  (          3          )                    
It can be understood from Equation (3) that the conventional LLRs each require two exponential calculations for each numerator and denominator, and the terms increase in number as an order of QAM increases.
Accordingly, a need exists for a system and method for reducing calculations for decoding in a mobile communication system.